SPOILERS AHEAD! BE WARNED!
What have you found?
Game Instructions: This is a random reward - though some story conclusions will generally give better results.
Estimating Echoes per Action
A thieves' cache! gets treasures with values 0-80. A Shrine of the Deep Blue Heaven gets treasures in the range 0-160. The average value of Uncovering an Unpredictable Treasure 0-80 is 27.03 Echoes; the average of 0-160 is 54.67 Echoes. This doesn't include other rewards that the expeditions may bring.
Thanks to the revamp that is Favours: The Docks, the number of actions which are spent on preparing for and undergoing expeditions can be better minimized than before. There is a guide for minimizing the number of actions for Shrine of the Deep expeditions, which can be read here. Incidentally, this type of expedition can yield any of the non-Fate rewards which have been listed above. It can also yield an Eyeless Skull instead of any of the above.
These options generate Connected: to the respective college of two plus one tenth the treasure value change points, and Making Waves change points of four plus half the treasure value. Hence, you may want to consider the exact treasure value before making the decision to donate.
Eyeless Skulls are not Unpredictable Treasures and cannot be donated.